EDIT: Ninjaed by Volt...
Phase stabilizers dont work across interstellar distances. If they would they would be insanely OP as it would allow you to bypass the requirement to jump to the star first. Phase stabilizers are already the probably most powerful technology in the entire game and it is an extremely painful job to deal with a Vasari using them with skill.
For the lore, if Phase stabilizers would work accross interstellar distances the Vasari would have probably outrun their enemy long ago. The huge distances between stars is far to much, even for high end vasari technology.
There is still a way to help you. Place a Phase stabilizer at your homestar and at your homeworld/often attacked planet. So you only have to jump to the star and then after only one more jump you are there for the rescue.^^